Topological Dirac nodal lines and surface charges in fcc alkaline earth metals

Abstract

In nodal-line semimetals, the gaps close along loops in k space, which are not at high-symmetry points. Typical mechanisms for the emergence of nodal lines involve mirror symmetry and the π Berry phase. Here we show via ab initio calculations that fcc calcium (Ca), strontium (Sr) and ytterbium (Yb) have topological nodal lines with the π Berry phase near the Fermi level, when spin–orbit interaction is neglected. In particular, Ca becomes a nodal-line semimetal at high pressure. Owing to nodal lines, the Zak phase becomes either π or 0, depending on the wavevector k, and the π Zak phase leads to surface polarization charge. Carriers eventually screen it, leaving behind large surface dipoles. In materials with nodal lines, both the large surface polarization charge and the emergent drumhead surface states enhance Rashba splitting when heavy adatoms are present, as we have shown to occur in Bi/Sr(111) and in Bi/Ag(111).

Universal phase transition and band structures for spinless nodal-line and Weyl semimetals

“…(ν 0 ; ν 1 ν 2 ν 3 ) = (0; 000) 16 , and it agrees with the number of TNLs, (n A , n B ) = (4, 0) in Ca and (n A , n B ) = (0, 6) in Yb.…”

“…First, we consider fcc Ca, whose space group is No. 225 16 . Ca have four type-A TNLs near each of the four TRIM L. The little group at the L points is D 3d which contains three C 2 -rotational operations.…”

“…In some cases, there are more than one TNLs in the Brillouin zone. Ca (calcium) has four type-A TNLs and and Yb (ytterbium) without the spin-orbit coupling has six pairs of type-B TNLs 16 . Let n A and n B denote the number of type-A TNLs and that of type-B TNLs, respectively.…”

“…Hence, the nodal lines are protected topologically. However, existence of characteristic surface states called drumhead surface states is not necessarily guaranteed 9,16 . The TNLSMs have been predicted theoretically in various materials with negligible spin-orbit interaction.…”

“…The TNLSMs have been predicted theoretically in various materials with negligible spin-orbit interaction. The candidates are carbon allotropes [17][18][19] , Cu 3 (Pd, Zn)N 20,21 , Ca 3 P 2 22,23 , LaN 24 , compressed black phosphorus 25 , alkaline-earth metals 16,26 , BaSn 2 27 , and CaP 3 family 28 . DC conductivities are calculated in hyperhoneycomb lattices with the TNLs 29,30 .…”